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We demonstrate the accuracy and stability of the proposed methods using numerical experiments of the Cahn Hilliard equation.
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Next we build a spatially heterogeneous structured model upon developing a reaction diffusion system; then, using numerical experiments we analyze some typical effects of spatial heterogeneities on the persistence or extinction of native or introduced and invading species.
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The results are validated using numerical experiments.
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Finally, we use numerical experiments with challenging problems of increasing complexity to illustrate the usage and benefits of regularization, addressing the questions above.
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